A clamping device for clamping a workpiece to a machine spindle includes at least one clamping bush which extends around a central axis and has at least one clamping surface for the workpiece and at least one clamping body. The clamping bush on a side remote from the clamping surface at least one support surface which extends about the central axis along a helical line. On a side facing, the clamping bush comprises at least one support surface which extends about the central axis along a helical line with a predefined pitch and is inclined at an angle of inclination to a direction axial to the central axis. The clamping body includes a hydraulic chamber in the interior of the clamping body. The clamping device also includes a displacement element, and at least one pressure generator. A clamping force is generatable between the clamping bush and workpiece.

A clamping device for clamping a workpiece to a machine spindle includes at least one clamping bush which extends around a central axis and has at least one clamping surface for the workpiece and at least one clamping body. The clamping bush on a side remote from the clamping surface at least one support surface which extends about the central axis along a helical line. On a side facing, the clamping bush comprises at least one support surface which extends about the central axis along a helical line with a predefined pitch and is inclined at an angle of inclination to a direction axial to the central axis. The clamping body includes a hydraulic chamber in the interior of the clamping body. The clamping device also includes a displacement element, and at least one pressure generator. A clamping force is generatable between the clamping bush and workpiece.